being only 15, were too young to go. They read the same books, mostly about mathematics, and by the time they were 17, they started to study mathematics on scholarships to Trinity in 1941. Both had already covered most of the undergraduate material. The two of them attended Part III lectures only and graduated with distinction in 1943.

Mathematics graduates were required in wartime Britain to support the war effort, and James was sent to work under Sydney Goldstein in the Aerodynamics Division of the National Physical Laboratory (NPL). James was initially fed up with that, for his girlfriend Nancy, also a Cambridge mathematician, had been sent to Farnborough on aerodynamics research work, and James would have liked a similar posting. Goldstein, whom James quickly learned to like and admire, used mathematics to illuminate details of aerodynamic flow. He took a great interest in James and inspired him, advising him to learn what he could about supersonic and viscous flow.

Before the war most supersonic flow and boundary layer work had been done and written up by German aerodynamicists. James quickly understood and extended their work and clearly liked it. The reports on that work, written by James at the NPL and later submitted to Trinity, gained him a Prize fellowship, allowing him to return to Cambridge and resume his research into pure mathematics. But he was beginning to appreciate applied mathematics almost as much, and many people whom James admired showed such interest and curiosity about his wartime work and what he might do for aerodynamics that he hardly had the inclination or time to resume his old life. He married Nancy before the end of the war and moved to Cambridge but would not stay there long, nor, finally, would he emerge as a pure mathematician.

Sydney Goldstein left the NPL to become professor at Manchester in 1946 and invited James to go there with him as a senior lecturer in mathematics. In accepting that post he implicitly accepted also the challenge of developing the mathematics most useful in aerodynamics. James did most things that Goldstein advised and usually took note of what Goldstein said. He shared with friends Goldstein’s speculation